On Iterative Unscented Kalman Filter using Optimization

The unscented Kalman filter (UKF) is a very popular solution for estimation of the state in nonlinear systems. Similar to the extended Kalman filter (EKF) and contrary to the Kalman filter (KF) for linear systems, the UKF provides no guarantees that the filter updates will improve the filtered state estimate. In the past, the iterated EKF (IEKF) has been suggested as a way to online monitor the filter performance and try to improve it using optimization techniques. In this paper we do the same for the UKF, deriving six iterated UKF (IUKF) variations based on two cost functions and three optimization algorithms. The methods are evaluated and compared to IEKF versions and to two versions of the iterative posterior linearization filter (IPLF) in three benchmark simulation studies. The results show that IUKF algorithms can be used as a derivative free alternative to IEKF, and provide insights about the different design choices available in IUKF algorithms.